RE: Optimum Spark Dwell Time

>Hi Mark,
>Yes, I would like to see the info and formulas on the dwell vs off time. 
> It is the one area of my spark gap design that I am unsure of.
Greetings Tesla Coilers,
        I thought this topic might generate some additional discussion so
have posted it to both listservers.  

                         Spark Gap Dwell Time
        A tesla coil primary consists of a capacitor and an inductor
(primary coil), separated by a spark gap, which is normally open circuited.
During this initial time interval the power supply charges up the capacitor
until the spark gap begins conducting.  Once the spark gap fires, the power
supply can be considered to be out of the circuit since it typically
supplies currents of .03 to 2 amps or so, while the currents circulating
between the capacitor and primary coil are on the order of 10's to 100's of
amperes.  As the energy in the primary circuit exchanges between the
capacitor and primary coil at their resonant frequency, a current is induced
in the secondary coil.  This current is proportional to M, the mutual
inductance between the primary and secondary coils.  
        More importantly, the coupling coefficient k=M/sqrt(Lp x Ls)
determines how effectively the energy is coupled to the secondary coil
(where Lp = primary coil self inductance, and Ls=secondary coil self
inductance).  Typical k values are 0.5-0.25 for conventional tesla coils,
and k>0.3 for magnifier systems.  If you observe the secondary current
waveform during this energy exchange, you see that the envelope of the
current waveform rises to a maximum, and then rings down much like a sinx/x
function.  This complex envelope exists because the secondary is oscillating
at three frequencies while the spark gap is conducting (assuming tight
coupling).  After the spark gap becomes non-conducting, the secondary slowly
rings down at its natural resonant frequency.
        The objective is to couple as much energy from the primary into the
secondary as possible, then quench (turn off) the spark and let the
secondary ring down.  The Corum brothers have studied this and have found
that the secondary current maximum occurs at a time t=1/(2 x k x F) where k
is the coupling coefficient, and F is the resonant frequency of the
primary/secondary.  At this point in time, the primary has coupled as much
energy as it can to the secondary.  The secondary current maximum occurs
when the primary current envelope is at its first minimum, which happens to
be a great time to quench the spark.  If the gap continues to conduct,
energy is coupled back and forth between the primary and secondary, and the
maximum secondary current is never achieved.  This is why lousy spark gaps
produce poor performance.
        The above equation is correct only in the case where there are
minimal resistive losses in the primary and secondary.  When resistance in
the circuit is present, this time interval gets shorter.  The equation now
has no simple analytical form like this either.  Typically, the largest
source of resistance is the spark gap.
        The net effect of all of this is that if you intend to use high
coupling coefficients (large k), you will need to have your spark gap turn
off quickly.  Typically, you will want to quench the spark in some tens of
microseconds.  Remember that the optimal time will be shorter that the
equation above suggests due to resistive losses.
        Note also that the above equation is frequency dependent.  Operating
your coil at a lower resonant frequency means you don't have to quench the
spark as quickly for good performance.  In addition, lower operating
frequencies make your coil less efficient radiators of RF.  This is usually
achieved by using a large toroid on the secondary to add capacitance to the
Mark S. Rzeszotarski
Mark S. Rzeszotarski, Ph.D., Senior Physicist, Radiology Dept.
The Mt. Sinai Medical Center, Cleveland, Ohio 44106
Assistant Professor, Case Western Reserve University
Departments of Radiology and Biomedical Engineering
Voice:216-421-4689  FAX:216-421-5343  E-mail:msr7-at-po.cwru.edu